This paper utilises distributional random forests as a flexible machine learning method for analysing income distributions. Distributional random forests avoid parametric assumptions, capture complex interactions among covariates, and, once trained, provide full estimates of conditional income distributions. From these, any type of distributional index such as measures of location, inequality and poverty risk can be readily computed. They can also efficiently process grouped income data and be used as inputs for distributional decomposition methods. We consider four types of applications: (i) estimating income distributions for granular population subgroups, (ii) analysing distributional change over time, (iii) spatial smoothing of income distributions, and (iv) purging spatial income distributions of differences in spatial characteristics. Our application based on the German Microcensus provides new results on the socio-economic and spatial structure of the German income distribution.